The optical system of a spectrometer projects the image of an illuminated slit onto a plane containing a detector. The formation of the image is governed by the usual issues of magnification and vignetting found in any optical system. Optimum resolution results from forming an aberration-free image at the detector plane.
Optimal use of a dispersive element, such as a diffraction grating or prism, requires that it be placed in a collimated portion of the optical system. This leads to a simplification in the analysis of the spectrometer optics, since the overall magnification is then determined by the ratio of the focal lengths of the focusing and collimating optics: M=F2/F1.
When the dispersive element is a reflective diffraction grating the optical path shown in FIG. 1 must be folded. To avoid chromatic aberration it is desirable to use reflective optics rather than lenses. The result is an optical train that contains at least three folds. A common arrangement for such a system is shown in FIG. 2, which depicts a symmetrical Czerny-Turner design.
The disadvantage of this system is that using spherical mirrors in a folded configuration introduces astigmatism, in which the effective focal length of the mirror in the plane of the fold (the tangential plane) is different from that in the perpendicular (or sagittal) plane. The on-axis focal length of a concave mirror is given by F=R/2, where R is the radius of curvature of the spherical surface. When used in an off-axis configuration the focal lengths in the tangential and sagittal planes become:Ft=R cos ø/2Fs=R/2 cos øwhere ø is the angle of incidence at the mirror. Thus, the focal length becomes shorter in the plane of dispersion (tangential) and longer in the perpendicular (sagittal) plane.
The ideal image of the slit at the detector plane is a magnified replica which reproduces both the width and height of the illuminated portion of the slit. To optimize resolution the width of the slit is focused, which is normally in the tangential plane of the system. The sagittal image comes to a focus behind the detector plane if left uncompensated, with the result that the image at the detector is blurred in the vertical direction. If the detector is not sufficiently large to accept the full size of the blurred vertical image a loss of sensitivity will result. If an exit slit is used in place of a detector and the height of the exit slit is insufficient to capture the entire vertical span then the throughput is reduced.
These issues are all well-known and have typically been addressed by designing spectrometers with the smallest possible fold angles, often at the cost of increasing the size and complexity of the spectrometer design. This classical approach minimizes but does not eliminate the problem. The current invention discloses an alternative and quite general method of addressing the astigmatism problem by eliminating it entirely.